Question: Why $\frac{|w-z|}{|1-\overline{w}z|} <1 $ for $w$ and $z$ in $D(0,1)=\{c \in \mathbb{C}: |c|<1 \}$?
Attempt: I know that this is quite trivial but I cannot compute it. I tried multiplying both the numerator and the denominator by $w$. The I got $\frac{|w-z|}{|w-|w|^2z|}$ but I do not know how to continue. Any help will be appreciated.
